Hasil untuk "Folklore"

Xiaotong Ji, Rasul Tutunov, Matthieu Zimmer et al.

Decoding sits between a language model and everything we do with it, yet it is still treated as a heuristic knob-tuning exercise. We argue decoding should be understood as a principled optimisation layer: at each token, we solve a regularised problem over the probability simplex that trades off model score against structural preferences and constraints. This single template recovers greedy decoding, Softmax sampling, Top-K, Top-P, and Sparsemax-style sparsity as special cases, and explains their common structure through optimality conditions. More importantly, the framework makes it easy to invent new decoders without folklore. We demonstrate this by designing Best-of-K (BoK), a KL-anchored coverage objective aimed at multi-sample pipelines (self-consistency, reranking, verifier selection). BoK targets the probability of covering good alternatives within a fixed K-sample budget and improves empirical performance. We show that such samples can improve accuracy by, for example, +18.6% for Qwen2.5-Math-7B on MATH500 at high sampling temperatures.

Shrikant Nandkumar

It is believed that from the earliest periods, the human species began to dramatically imitate the actions of animals. This natural behaviour pattern can be traced to tribal and folk art, such as painting, music, dance, and dance theatre. ‘Chau’, often spelt as ‘Chhau’ by some Indian authors, is a dance and dance-theatre form from the eastern region of India; it is one of the significant examples of how animal movements and subsequent nature patterns primarily impact dance patterns and their presentation. Chau is one of the famous traditional theatres of India, often categorized as semi-classical dance theatre, mainly because of its movement vocabulary. This article aims to examine and discuss how such patterns emerged and how they hold significance in shaping these movements. While Chau adapted technicality in its presentation and instrumentation, its core and legacy remain unchanged – namely, its movement vocabulary pattern and folklore-mythology.

Ramona Maria MIHĂILESCU

Today, customs continue to preserve their old functions and forms, but along with traditional customs, new customs appear as a response to the new living conditions. The customs have lost much of their ritual values, emphasizing the ceremonial, artistic ones. The changes felt in today's Romanian village are obvious, especially after the Second World War. An indissoluble link is formed between tradition and innovation, the former not excluding the path to progress. In today's times, the creator comes out of isolation thanks to the mass media, the possibility to travel both in the country and abroad, to participate in various folk-art fairs, thus having the privilege of creating new artistic forms in response to current needs, these being no longer the same for all social categories. Folklore is a living phenomenon, therefore in constant transformation, all folklore categories being characterized by mobility.

Minkyu Kim

Let $k$ be a unital commutative ring. In this paper, we study polynomial functors from the category of finitely generated free nilpotent groups to the category of $k$-modules, focusing on comparisons across different nilpotency classes and polynomial degrees. As a consequence, we obtain refinements of parts of the results of Baues and Pirashvili on polynomial functors over free nilpotent groups of class at most 2, which also recover several folklore results for free groups and free abelian groups. Furthermore, we investigate a modular analogue, formulated using dimension subgroups over a field of positive characteristic instead of lower central series. To prove the main results, we establish general criteria that guarantee equivalences between the categories of polynomial functors of different degrees or with different base categories. They are described by using a two-sided ideal of a monad associated with the base category, which encodes polynomiality of a specific degree. Inspired by the main results, we also investigate an analogous ideal for analytic functors, and show that, in most cases, no such an ideal exists.

Guglielmo Nocera, Morena Porzio

Let $G$ be a complex reductive group. A folklore result asserts the existence of an $\mathbb{E}_2$-algebra structure on the Ran Grassmannian of $G$ over $\mathbb{A}^1_{\mathbb{C}}$, seen as a topological space with the complex-analytic topology. The aim of this paper is to prove this theorem, by establishing a homotopy invariance result: namely, an inclusion of open balls $D' \subset D$ in $\mathbb{C}$ induces a homotopy equivalence between the respective Beilinson--Drinfeld Grassmannians $\mathrm{Gr}_{G, {D'}^n} \hookrightarrow \mathrm{Gr}_{G, D^n}$, for any positive integer $n$. We use a purely algebraic approach, showing that automorphisms of a complex smooth algebraic curve $X$ can be lifted to automorphisms of the associated Beilinson--Drinfeld Grassmannian. As a consequence, we obtain a stronger version of the usual homotopy invariance result: namely, the homotopies can be promoted to equivariant stratified isotopies, where "equivariant" refers to the action of the arc group $\mathrm{L}^+G$ and "stratified" refers to the stratification induced by the Schubert stratification of $\mathrm{Gr}_G$ and the incidence stratification of $\mathbb{C}^n$.

Sławomir Dadas, Małgorzata Grębowiec, Michał Perełkiewicz et al.

Large language models (LLMs) are becoming increasingly proficient in processing and generating multilingual texts, which allows them to address real-world problems more effectively. However, language understanding is a far more complex issue that goes beyond simple text analysis. It requires familiarity with cultural context, including references to everyday life, historical events, traditions, folklore, literature, and pop culture. A lack of such knowledge can lead to misinterpretations and subtle, hard-to-detect errors. To examine language models' knowledge of the Polish cultural context, we introduce the Polish linguistic and cultural competency benchmark, consisting of 600 manually crafted questions. The benchmark is divided into six categories: history, geography, culture & tradition, art & entertainment, grammar, and vocabulary. As part of our study, we conduct an extensive evaluation involving over 30 open-weight and commercial LLMs. Our experiments provide a new perspective on Polish competencies in language models, moving past traditional natural language processing tasks and general knowledge assessment.

Lawrence Hollom

The bunkbed conjecture, which has featured in the folklore of probability theory since at least 1985, concerns bond percolation on the product graph $G\Box K_2$. We have two copies $G_0$ and $G_1$ of $G$, and if $x^{(0)}$ and $x^{(1)}$ are the copies of a vertex $x\in V(G)$ in $G_0$ and $G_1$ respectively, then edge $x^{(0)}x^{(1)}$ is present. The conjecture states that, for vertices $u,v\in V(G)$, percolation from $u^{(0)}$ to $v^{(0)}$ is at least as likely as percolation from $u^{(0)}$ to $v^{(1)}$. While the conjecture is widely expected to be true, having attracted significant attention, a general proof has not been forthcoming. In this paper we consider three natural generalisations of the bunkbed conjecture; to site percolation, to hypergraphs, and to directed graphs. Our main aim is to show that all these generalisations are false, and to this end we construct a sequence of counterexamples to these statements. However, we also consider under what extra conditions these generalisations might hold, and give some classes of graph for which the bunkbed conjecture for site percolation does hold.

Hideki Miyachi

The $L^1$-$L^\infty$ geometry is the Finsler geometry of the Teichmüller space by the Teichmüller metric and the $L^1$-norm function of holomorphic quadratic differentials. In this paper, aiming to develop the $L^1$-$L^\infty$-geometry and the differential geometry on the Teichmüller space, we formulate the second order infinitesimal structures (the infinitesimal structures on the (co)tangent bundles) over the Teichmüller space. We will give model spaces of the second order infinitesimal spaces. By applying our formulation, we give affirmative answers to two folklore. We first show that the map from the space of holomorphic quadratic differentials to the tangent bundle defined by Teichmüller Beltrami differentials is a real-analytic diffeomorphism on every stratum in the space of holomorphic quadratic differentials. Second, we show that the Teichmüller metric is real-analytic on the image of each stratum. We also observe a new duality between the Teichmüller metric and the $L^1$-norm function at the infinitesimal level.

T. Tony Cai, Abhinav Chakraborty, Lasse Vuursteen

This paper studies federated learning for nonparametric regression in the context of distributed samples across different servers, each adhering to distinct differential privacy constraints. The setting we consider is heterogeneous, encompassing both varying sample sizes and differential privacy constraints across servers. Within this framework, both global and pointwise estimation are considered, and optimal rates of convergence over the Besov spaces are established. Distributed privacy-preserving estimators are proposed and their risk properties are investigated. Matching minimax lower bounds, up to a logarithmic factor, are established for both global and pointwise estimation. Together, these findings shed light on the tradeoff between statistical accuracy and privacy preservation. In particular, we characterize the compromise not only in terms of the privacy budget but also concerning the loss incurred by distributing data within the privacy framework as a whole. This insight captures the folklore wisdom that it is easier to retain privacy in larger samples, and explores the differences between pointwise and global estimation under distributed privacy constraints.

Ka Hei Carrie Lau, Bhada Yun, Samuel Saruba et al.

Oral traditions, vital to cultural identity, are losing relevance among youth due to the dominance of modern media. This study addresses the revitalization of these traditions by reconnecting young people with folklore. We introduce Anansi the Spider VR, a novel virtual space that combines first-person virtual reality (VR) with generative artificial intelligence (Gen-AI)-driven narrative personalization. This space immerses users in the Anansi Spider story, empowering them to influence the narrative as they envision themselves as the `protagonists,' thereby enhancing personal reflection. In a 2 by 2 between-subjects study with 48 participants, we employed a mixed-method approach to measure user engagement and changes in interest, complemented by semi-structured interviews providing qualitative insights into personalization and immersion. Our results indicate that personalization in VR significantly boosts engagement and cultural learning interest. We recommend that future studies using VR and Gen-AI to revitalize oral storytelling prioritize respecting cultural integrity and honoring original storytellers and communities.

Nachiketa Adhikari, Yun Shi

We show that any $(-2)$-shifted symplectic derived scheme $\textbf{X}$ (of finite type over an algebraically closed field of characteristic zero) is locally equivalent to the derived intersection of two Lagrangian morphisms to a $(-1)$-shifted symplectic derived scheme which is the $(-1)$-shifted cotangent stack of a smooth classical scheme. This leads to the possibility of the following viewpoint that is, at least to us, new: any $n$-shifted symplectic derived scheme can be obtained, locally, by repeated derived Lagrangian intersections in a smooth classical scheme. We also give a separate proof of our main result in the case where the local Darboux atlas cdga for $\textbf{X}$ has an even number of generators in degree $(-1)$; in this case we strengthen the result by showing that $\textbf{X}$ is in fact locally equivalent to the derived critical locus of a shifted function, which we've been told is a folklore result in the field. We indicate the implications of this for derived moduli stacks of sheaves on Calabi-Yau fourfolds by spelling out the case when the fourfold is $\mathbb{C}^4$.

David Conlon, Jacob Fox, Benjamin Gunby et al.

A fundamental problem in Ramsey theory is to determine the growth rate in terms of $n$ of the Ramsey number $r(H, K_n^{(3)})$ of a fixed $3$-uniform hypergraph $H$ versus the complete $3$-uniform hypergraph with $n$ vertices. We study this problem, proving two main results. First, we show that for a broad class of $H$, including links of odd cycles and tight cycles of length not divisible by three, $r(H, K_n^{(3)}) \ge 2^{Ω_H(n \log n)}$. This significantly generalizes and simplifies an earlier construction of Fox and He which handled the case of links of odd cycles and is sharp both in this case and for all but finitely many tight cycles of length not divisible by three. Second, disproving a folklore conjecture in the area, we show that there exists a linear hypergraph $H$ for which $r(H, K_n^{(3)})$ is superpolynomial in $n$. This provides the first example of a separation between $r(H,K_n^{(3)})$ and $r(H,K_{n,n,n}^{(3)})$, since the latter is known to be polynomial in $n$ when $H$ is linear.

P. A. Levina, Michael А. Perepelkin

This article is an experience of studying the structure and role of the «Samara text» in the novel «Petrushka's Syndrome» by Dina Rubina. The initial premise of this article is the author's conviction that it is space that appears in the named novel by Dina Rubina as a constructive principle of the literary work genre organization and the construction of an artistic semiosphere, through analysis of which the researcher can enter the sphere of meanings. The Samara space is not the only one in the novel and is included in a large and complex system of spaces formed by the «Lviv», «Prague», «Berlin», «Israeli» and «South Sakhalin» chapters, and each of these loci has its own artistic tasks and own meanings. At the same time, Samara appears in the novel as a very special space and semantic code formed by the Samara history, urban folklore, artistic and other texts, which together form an urban myth and urban text, and finally, perhaps, by Dina Rubina’s personal impressions, obviously well acquainted with Samara and the Samara residents. All these components of the «Samara text» form the Samara code, which is the focus of the article authors. The most thorough analysis in the article is one of the Samara mini-topos – Visi's apartment, which is the quintessence of the «Samara» life in the novel.

Xiang Li, Long Lan, Husam Lahza et al.

(Aim) Dragon Boat Racing, a popular aquatic folklore team sport, is traditionally held during the Dragon Boat Festival. Inspired by this event, we propose a novel human-based meta-heuristic algorithm called dragon boat optimization (DBO) in this paper. (Method) It models the unique behaviors of each crew member on the dragon boat during the race by introducing social psychology mechanisms (social loafing, social incentive). Throughout this process, the focus is on the interaction and collaboration among the crew members, as well as their decision-making in different situations. During each iteration, DBO implements different state updating strategies. By modelling the crew's behavior and adjusting the state updating strategies, DBO is able to maintain high-performance efficiency. (Results) We have tested the DBO algorithm with 29 mathematical optimization problems and 2 structural design problems. (Conclusion) The experimental results demonstrate that DBO is competitive with state-of-the-art meta-heuristic algorithms as well as conventional methods.

Robert J. Lemke Oliver

A folklore conjecture asserts the existence of a constant $c_n > 0$ such that $\#\mathcal{F}_n(X) \sim c_n X$ as $X\to \infty$, where $\mathcal{F}_n(X)$ is the set of degree $n$ extensions $K/\mathbb{Q}$ with discriminant bounded by $X$. This conjecture is known if $n \leq 5$, but even the weaker conjecture that there exists an absolute constant $C\geq 1$ such that $\#\mathcal{F}_n(X) \ll_n X^C$ remains unknown and apparently out of reach. Here, we make progress on this weaker conjecture (which we term the "uniform exponent conjecture") in two ways. First, we reduce the general problem to that of studying relative extensions of number fields whose Galois group is an almost simple group in a natural primitive permutation representation. Second, for almost all such groups, we prove the strongest known upper bound on the number of such extensions. These bounds have the effect of resolving the uniform exponent conjecture for solvable groups, sporadic groups, exceptional groups, and classical groups of bounded rank.

Luigi Santocanale, Cédric de Lacroix, Gregory Chichery

For a functor $Q$ from a category $C$ to the category $Pos$ of ordered sets and order-preserving functions, we study liftings of various kind of structures from the base category $C$ to the total(or Grothendieck) category $\int Q$. That lifting a monoidal structure corresponds to giving some lax natural transformation making $Q$ almost monoidal, might be part of folklore in category theory.We rely on and generalize the tools supporting this correspondence so to provide exact conditions for lifting symmetric monoidal closed and star-autonomous structures.A corollary of these characterizations is that, if $Q$ factors as a monoidal functor through $SLatt$, the category of complete lattices and sup-preserving functions, then $\int Q$ is always symmetric monoidalclosed. In this case, we also provide a method, based on the double negation nucleus from quantale theory, to turn $\int Q$ into a star-autonomous category.The theory developed, originally motivated from the categories $P-Set$ of Schalk and de Paiva, yields a wide generalization of Hyland and Schalk construction of star-autonomous categories by means of orthogonality structures.

Elena N. Vaganova

Introduction. Lamentations remain an enduring national treasure of the Mordovian ethnos. They do not only offer the richest cultural and historical information, but also represent a living existence of the past in modern times. Based on the research and the folklore material, it gives a generalized characteristic of poetic devices and visual and expressive means used in the texts of the lamentations of the funeral and memorial cycle of Mordva-Erzya. Materials and Methods. The study combines methods of description and comparative analysis. The basis of the empirical material was reliable folklore collections with exceptional historical, cultural and research value, borrowed from the oral and poetic creativity of the Mordovian people, the vocabulary of the Erzya language, traditions and rituals. Results and Discussion. Lamentations is the most important component of the verbal and musical codes of the funeral and memorial complex. The poetry of lamentation, which has preserved archaic features, gives the national culture a special charm, emphasizes its lively sound, primordial independence and originality. Lamentations are used to express grief at the loss of a beloved one, and they are characterized by a well-developed system of comparisons and metaphors that perform the functions of imagery and allegory. Special colorfulness, brightness and expressiveness in lamentations are given by the traditional techniques widely used in lamentations: appeals, comparisons, metaphors, artistic parallelisms and other visual and expressive means. Conclusion. The Mordovian religious tradition is rich in means of expression and poetic techniques, the functioning of which in the structure of folklore work gives its best samples a unique national flavor. The manner of performing lamentations has local traditions, lamentable melodies typical for a particular locality. The considered images, motives, appeals, comparisons, metaphors, personifications, contribute to understanding the depth of the spiritual world of the people, their worldview.

Chandrachur Chakraborty, Parthasarathi Majumdar

Inspired by the reported existence of substantive magnetic fields in the vicinity of the central supermassive black holes in Sagitarius A* and Messier 87*, we consider test particle motion in the spacetime close to a generic spherical black hole in the presence of magnetic fields in its vicinity. Modelling such a spacetime in terms of an axisymmetric, non-rotating Ernst-Melvin-Schwarzschild black hole geometry with appropriate parameters, we compute the geodesic nodal-plane precession frequency for a test particle with mass, for such a spacetime, and obtain a non-vanishing result, surpassing earlier folklore that only axisymmetric spacetimes with rotation (non-vanishing Kerr parameter) can generate such a precession. We call this magnetic field-generated phenomenon Gravitational Larmor Precession. What we present here is a Proof of Concept incipient assay, rather than a detailed analysis of supermassive black holes with magnetic fields in their neighbourhood. However, for completeness, we briefly discuss observational prospects of this precession in terms of available magnetic field strengths close to central black holes in galaxies.

Aysun Ezgi Yılmaz

Nowadays, factors, such as the world’s being a global village and the fast living of the consumption age together with the developing technology have led to the elimination of cultural values. In this era, which detains individuals from listening to, reading and producing, the cinema is considered to be an effective tool for preventing the present cultural erosion as it is suitable for the consumer’s nature by combining the words and texts with the visual elements. In this context, the subject of this research “Iftarlık Gazoz”, written and directed by Yüksel Aksu, serves as an example with the cultural elements it contains for their transfer and protection. The movie was supported by Ministry of Culture and Tourism and when the folkloric elements in the movie (masterapprentice relationship, folk songs, mani, proverbs etc.) were examined it can be seen that these elements are not placed irrelevantly; instead, they are aproduct of a conscious culture protection approach. The movie examined here has been evaluated by taking into consideration the cultural elements it has in the context of The Convention for the Safeguarding of the Intangible Cultural Heritage and The Convention on the Protection and Promotion of the Diversity of Cultural Expressions, which were signed for avoiding the standardization in culture.

Eleonora F. Shafranskaya, Tatyana V. Volokhova

The article deals with the problem of orientalism in literature, narrowed to the question of Russian orientalism and its Soviet derivation. The names of Nikolai Karazin and Andrey Platonov are mentioned among Russian literary Orientalists. The researchers identify the differences between Soviet Orientalism and the Orientalism of the XIX century. The analytical paradigm presented in the article outlines the prospects for the scientific study of Uzbek impressions. Salir-Gul (1933) by Sigismund Krzyzanowski and Pavel Zaltzman's novel Central Asia in the Middle Ages (1930s). For the first time, the novel The nomad (Kochevye) by the Russian writer of the twentieth century Leonid Solovyov written in 1929 and published in 1932 is analyzed in detail. Appeal to the folklore, ceremonial, and ritual life of the peoples of Central Asia becomes one of the main techniques of Leonid Solovyov's Oriental poetics. Solovyov's narrator is not a traditional orientalist observer of an alien, and therefore exotic, picture of the world. In Solovyov's poetics, the subject of the story merges with its object and represents a single whole: Russian literature spoke in the voice of a stranger. The material of the article corresponds to the intentions outlined in modern postcolonial studies.